Did you know that different parts of a muscle are controlled by different nerves? The biceps has a long and a short head. Nerve cells connected to the long head's outer (lateral) part are activated during elbow flexion, while nerve cells connected to the inner (medial) part are activated by turning the wrist outwards (supination). When combining flexion and supination, nerve cells connected to the central part of the biceps are also activated.
Also, the long head is used more in the beginning of elbow flexion, whereas the short head is used more in the end (when elbows are more flexed). Thus you can place emphasis on different parts of the biceps with different exercises.

The EBT takeaway: When doing dumbbell curls, make sure you twist your wrist (so you pinky moves towards you face) to activate the inner and central parts of the biceps. To challenge the short head, use exercises that provide relatively more resistance when the elbow is flexed, such as cable curls. We personally do 3 sets of 10-12 reps of dumbbell curls and 3 sets of 10-12 reps of cable curls per week.
THE EVIDENCE: Schoenfeld BJ. The mechanisms of muscle hypertrophy and their application to resistance training. J Strength Cond Res. 2010;24(10):2857-72.